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There are two general patterns that could be used to express the desire that something had happened or had been done. One can—as far as I know—only be used when speaking in the first person, while the second can be adapted to other viewpoints.

The first relies upon the expression ojalá hubiera, and works as follow:

gustaría & desearía are the conditional forms of their respective verbs.

Again, certain modifiers may precede the word haber.

This pattern doesn't carry a sense of remorse to any major degree. It generally has the nuance of a reflection, but adverbs of magnitude could be used to help express the gravity of the statement.

These are general grammatical patterns that should be more or less understood everywhere. There are probably more idiomatic phrases in use throughout Latin America, but I couldn't think of any specifically.